Proves that rotationally and reflection symmetric compact noncollapsed ancient 3D Ricci flow solutions are either spheres or have unique asymptotics as t to -∞ with explicit description.
A collapsing ancient solution of mean curvature flow in $\mathbb{R}^3$
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We construct a compact, convex ancient solution of mean curvature flow in $\mathbb R^{n+1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $\pi$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies in a slab of width $\pi$ and in no smaller slab.
fields
math.DG 2years
2019 2verdicts
UNVERDICTED 2representative citing papers
An expository paper that presents and simplifies Wang's structure theory for convex ancient mean curvature flow solutions and shows rigidity results follow from it, including a new corollary.
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Unique asymptotics of ancient compact non-collapsed solutions to the 3-dimensional Ricci flow
Proves that rotationally and reflection symmetric compact noncollapsed ancient 3D Ricci flow solutions are either spheres or have unique asymptotics as t to -∞ with explicit description.
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Convex ancient solutions to mean curvature flow
An expository paper that presents and simplifies Wang's structure theory for convex ancient mean curvature flow solutions and shows rigidity results follow from it, including a new corollary.